。
She explained that matter to me.
Literal
She [topic-は] me [to-に] that matter [about-について] explained.
A clean illustration of the compound particle ~について ('about, concerning') — used to introduce the topic of communication. その事について then sets the topic for 説明する. Compared with bare に (which would be a flat dative), について explicitly frames the noun as the subject matter being discussed. 事 ('matter, thing, fact') is the abstract event/situation noun, distinct from 物 ('physical thing'). The particle is highly productive: 環境問題について ('about environmental issues'), 君について ('about you').